##### finding the max or min of a quadratic function

 Algebra Tutor: None Selected Time limit: 1 Day

answer the questions below about the quadratic function

g(x)=x²+8+18

a. does the function have a minimum or maximum value

b. what is the function's min or max value

c. where does it occur  x=

Oct 10th, 2015

Thank you for the opportunity to help you with your question!

g(x)=x²+8x+18

NB I am assuming that you erroneously ignored the x in 8x.

a.

To determine whether the function has a maximum or minimum, we differentate it twice i.e

first derivative, g'(x) = 2x+8

Second derivative, g"(x) = 2

Therefore the function has a minimum point since the second derivative is positive i.e (+2)

b.

The function minimum point is the point where the slope/gradient of the function is equal to zero.

The slope/gradient of the function is given by the first derivative

Therefore, g'(x) = 2x+8 = 0

2x =-8 hence x=-4

Substituting the value of X into the equation gives

g(x) = (-4)^2+8(-4)+18 = 2

Therefore the functions minimum point is 2

c.

As calculated above, the function's minimum point occurs at the point where x= -4

Let me know if my assumption of instituting x into the function was right or wrong.Regards.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 10th, 2015

...
Oct 10th, 2015
...
Oct 10th, 2015
Dec 6th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer